Final answer:
The interest earned would be $58.986.
To find the interest earned, we subtract the principal amount (P) from the total amount (A):
Interest earned = $158.986 - $100 = $58.986
Step-by-step explanation:
To calculate the compound interest, we can use the formula A = P(1 + r/n)^(nt), where:
- A is the total amount including interest
- P is the principal amount (initial investment)
- r is the annual interest rate (expressed as a decimal)
- n is the number of times that interest is compounded per year
- t is the number of years
In this case, Libby saved $100, so the principal amount (P) is $100. The interest rate (r) is 2.5% or 0.0256 as a decimal. The interest is compounded annually, so the number of times that interest is compounded per year (n) is 1. The time period (t) is 20 years.
Using the formula:
A = 100(1 + 0.0256/1)^(1 * 20)
A = 100(1.0256)^(20)
A = 100(1.5898581)
A = $158.986
To find the interest earned, we subtract the principal amount (P) from the total amount (A):
Interest earned = $158.986 - $100 = $58.986